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An n-digit number is a positive numbe...

An n-digit number is a positive number with exactly `n` digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5, and 7. The smallest value of `n` for which this is possible is a.`6` b. `7` c. `8` d. `9`

A

6

B

7

C

8

D

9

Text Solution

Verified by Experts

The correct Answer is:
B
Each place can be filled in 3 ways
`therefore ` n places can be filled in `3^(n) therefore 3^(n) ge 900`
`therefore 3^(6)=729` and `3^(7)=2187" " `Hence n = 7.
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